Question

Solve the following quadratic equation.

8x² + 2x + 1 = 0

Answer 1

Comparing the equation 8x² + 2x + 1 = 0 with ax² +bx + c = 0, we have,

a = 8, b = 2, c = 1

∴ b² – 4ac = (2)² – 4(8)(1)

= 4 – 32

= – 28 < 0

So, the given equation has complex roots. These roots are given by

x = `(-"b" ± sqrt("b"^2 - 4"ac"))/(2"a")`

= `(-2 ± sqrt(-28))/(2(8))`

= `(-2 ± 2sqrt(7)"i")/16`

= `(-1 + sqrt(7)"i")/8`

Hence, the roots of the equation are

`(-1 + sqrt(7)"i")/8` and `(-1 - sqrt(7)"i")/8`.